How does mantle convection cause plate tectonics

They have gradually moved over the course of hundreds of millions of years—alternately combining into supercontinents and pulling apart in a process known as continental drift.

The supercontinent of Pangaea formed as the landmasses gradually combined roughly between and mya. It is widely accepted by scientists today.

Earthquakes and volcanoes are the short-term results of this tectonic movement. The long-term result of plate tectonics is the movement of entire continents over millions of years Fig. The presence of the same type of fossils on continents that are now widely separated is evidence that continents have moved over geological history.

Evaluate and interpret several lines of evidence for continental drift over geological time scales. The shapes of the continents provide clues about the past movement of the continents. The edges of the continents on the map seem to fit together like a jigsaw puzzle. For example, on the west coast of Africa, there is an indentation into which the bulge along the east coast of South America fits.

The shapes of the continental shelves—the submerged landmass around continents—shows that the fit between continents is even more striking Fig. Some fossils provide evidence that continents were once located nearer to one another than they are today.

Fossils of a marine reptile called Mesosaurus Fig. Another example is the fossil plant called Glossopteris, which is found in India, Australia, and Antarctica Fig. The presence of identical fossils in continents that are now widely separated is one of the main pieces of evidence that led to the initial idea that the continents had moved over geological history.

Evidence for continental drift is also found in the types of rocks on continents. There are belts of rock in Africa and South America that match when the ends of the continents are joined. Mountains of comparable age and structure are found in the northeastern part of North America Appalachian Mountains and across the British Isles into Norway Caledonian Mountains.

These landmasses can be reassembled so that the mountains form a continuous chain. Evidence from glacial striations in rocks, the deep grooves in the land left by the movement of glaciers, shows that mya there were large sheets of ice covering parts of South America, Africa, India, and Australia.

These striations indicate that the direction of glacial movement in Africa was toward the Atlantic ocean basin and in South America was from the Atlantic ocean basin. This evidence suggests that South America and Africa were once connected, and that glaciers moved across Africa and South America. There is no glacial evidence for continental movement in North America, because there was no ice covering the continent million years ago.

North America may have been nearer the equator where warm temperatures prevented ice sheet formation. Mid-ocean ridges or spreading centers are fault lines where two tectonic plates are moving away from each other. Mid-ocean ridges are the largest continuous geological features on Earth. They are tens of thousands of kilometers long, running through and connecting most of the ocean basins. Oceanographic data reveal that seafloor spreading is slowly widening the Atlantic ocean basin, the Red Sea, and the Gulf of California Fig.

The gradual process of seafloor spreading slowly pushes tectonic plates apart while generating new rock from cooled magma. However, the behaviour of these models exhibits considerable complexity and by restricting the number of intricacies included in the models we have been able to isolate, rather than obscure, the novel physics that results from the feedback between two fundamental features of mantle convection that regulate temperature with different timescales, namely, the presence of plates and internal heating.

Recent advances have been made in developing formulations that allow plate-like behaviour to evolve in mantle convection models without imposed geometrical constraints on the plate geometry, both in 2-D Richards et al. However, these models have not yet been successful in exhibiting long-timescale plate-like behaviour in high-Rayleigh-number calculations.

We have implemented an alternative approach to investigating whole-mantle convection over billion-year timescales that makes the study of such problems feasible with existing resources. The models give insight into the effects of plates on mantle convection given the restriction of a non-evolving plate geometry. Although limiting, this restriction allows for a first-order investigation of the interaction between multiple plates with dynamically evolving velocities and high-Rayleigh-number mantle convection.

The failure of infinite Prandtl number convection to exhibit plate-like behaviour when either uniform material properties or temperature-dependent rheologies are specified has been widely described e. In general, plate-like surface velocities are obtained in convection models only when a plate generation method is implemented. The plate-like surface motions achieved in these models are obtained by imposing surface velocity as a time-dependent boundary condition e.

We model thick lithospheric plates by specifying a highly viscous layer at the top of the mantle the model plates to emulate the high viscosity of the mantle's cold upper thermal boundary layer. Below this layer, we specify either a uniform viscosity or a viscosity that increases with depth. In all cases, the model plates are times more viscous than the material at their base and extend to a dimensional depth of approximately km assuming a model depth of km.

Plate geometries are specified a priori and remain fixed for the duration of each model run. The uniform velocity of tectonic plate interiors and the corresponding discontinuities in velocity at plate boundaries are emulated by prescribing surface velocity boundary conditions based on a force balance approach Gable et al.

This approach for prescribing plate velocities requires the integrated shear traction on the base of a plate to vanish at all times. The resulting condition is consistent with a strong rigid plate distributing the applied stresses.

By balancing the forces on each plate at each time step, evolving plate motion is obtained that is in dynamic equilibrium with the thermally induced forces driving convection. A hybrid spectral finite difference scheme previously described by Gable et al. The code has been benchmarked against other numerical models for a variety of problems that do not include plates and shows excellent agreement in those cases e. Travis et al. In addition, the plate model we utilize has been compared with material methods and power law rheology plate generation methods and the agreement between the surface heat flux and plate velocities of these models is excellent King et al.

This study focuses on three types of models: per cent basally heated isoviscous convection which we have designated Case A , isoviscous convection including internal heat sources designated Case B and convection with a depth-dependent viscosity and internal heat sources Case C.

In order to make a meaningful comparison of models with different viscosity structures and heating modes we have attempted to match the time-averaged mean surface heat flux from the three reference cases within the limits of the problem.

Consequently, if q b varies, as is the case when an isothermal bottom boundary is employed, surface heat flux varies similarly. Nearly all of the models presented in this study are characterized by isothermal boundaries. Since the Earth's plates have a mean thickness of roughly — km, we have chosen to restrict our study to investigating models with mean upper thermal boundary layer thicknesses in this range.

We have chosen to use the heat flux from a per cent basally heated isoviscous model Case A as a reference value. Keeping the ratio of Ra H to Ra B fixed at 15 discussed below we made a systematic search of Ra B , Ra H parameter space and identified a Rayleigh number pair that would give the same heat flux as the Case A model for each of the Cases B and C rheologies. There is an important restriction that accompanies this methodology.

Heat flow is affected by convection cell aspect ratio. Thus, if we want to compare models with similar heat fluxes we should match single-cell flow models with the same aspect ratio. The mean temperature and heat flux obtained for Cases A, B and C vary differently for free-slip and no-slip boundary conditions and models that include plates. In addition, the variation is dependent on aspect ratios. Consequently, we are required to match heat fluxes in a model with a specific aspect ratio.

We have chosen to match the heat fluxes from the three reference cases in an aspect ratio 3 geometry incorporating a single plate Table 1 , Models A3, B3 and C3. The reasons for this choice are two-fold. First, in all three reference cases a single-cell solution is obtained for this aspect ratio when a viscous plate is specified.

Second, the mean plate width in the majority of the multiple-plate models we will study is 3d. Thus, by fixing the heat flux obtained from an aspect ratio 3 model at a specific value, we will be able to test whether heat flow will remain similar in different aspect ratio models when the average plate size in the models is the same.

Moreover, if there is a difference, it will be clear whether this is related to the heating mode or to the rheology. To isolate the effect of internal heating we have examined several additional models that are heated entirely from within. These models are characterized by the same viscosity structure and heating rates as the Case C models; however, the bottom boundary of the models is insulating rather than isothermal.

However, mean temperature in per cent internally heated models is a function of model geometry and is discussed below. R: Model characterized by flow reversals.

Model names indicate the convection mode case A, B or C followed by the model aspect ratio plate width. Case A and Case B convection models are isoviscous.

Case C models have a viscosity that increases with depth by a factor of The values specified for Case A, B and C models are 10 7 , 0 , 1. Both vertical and horizontal grid spacing are uniform in all models. Second moment values are also given for and q s. Using eq. This heating rate is roughly in agreement with the estimated heating rates of chondritic meteorites Stacey The viscosity model used is characterized by a factor of 36 increase in viscosity with depth, with the highest gradient occurring in a depth range of — km.

The models in this paper were run for a minimum of 0. When scaled to Earth's mantle, this corresponds to a minimum of billion years. It is well known that high-Rayleigh-number, internally heated convection does not achieve a steady-state solution e. In the calculations reported in this work there is little variation in the moving average of the plate velocity or surface heat flow time-series using a time window that is 0.

In general, there are not discernible periodic patterns in these time-series even though the maximum and minimum values in each time-series are well defined. Before analysing any of the models that incorporate plates we shall compare the behaviour of the three reference cases when free-slip boundary conditions are prescribed. The purpose of examining the free-slip models is to determine the differences that exist in the cases strictly due to varying the heating modes and rheology.

We shall also compare the differences that exist between the reference cases when different aspect ratios are prescribed unit aspect ratio versus aspect ratio 12 models. In Fig. These models are referred to as Models A1-fs, B1-fs and C1-fs, and correspond to the reference cases A, B and C, respectively, for models where a unit aspect ratio calculation with reflecting sidewalls and free-slip top and bottom boundary conditions are prescribed. In order to maintain a similar degree of vigour in the models we adjust the Rayleigh numbers while adding internal heating and depth-dependent viscosity.

In Model C1-fs, the addition of depth-dependent viscosity re-establishes single-cell flow; however, the flow remains highly time-dependent. Also included in the table are second-moment values for and q s. We calculate the second moments once the models have reached a statistically steady state. The second-moment values are calculated by integrating the values obtained from the square of the difference of the time-series values and their mean. This value is divided by the integral of the mean over the same period.

Larger values for a particular second moment indicate that the time-series of the quantity fluctuates from its mean value by a greater amount than a quantity with a smaller second moment. The table shows that for any given aspect ratio the addition of internal heating increases the mean temperature of the models in calculations both with and without plates.

The time-averaged surface heat fluxes obtained from the free-slip isoviscous cases agree fairly closely for the unit aspect ratio model geometry Models A1-fs and B1-fs ; however, the heat flux obtained for Model C1-fs is almost 25 per cent lower than that obtained from Models A1-fs and B1-fs. The contrast in these heat flux trends differs in the models that include plates and is also a function of model aspect ratio.

In practice, we find that this is not the case. We find that q s — q b varies between In the latter cases, where periodicity appears absent, time averages may be above or below 15 for unpredictable periods. The values of q s — q b included in the tables indicate the average heating rate during the period in which and q s are calculated. These three models illustrate examples of Case A, B and C convection, respectively, in aspect ratio 12 boxes with periodic wrap-around vertical boundary conditions and free-slip surface boundary conditions.

Model Afs generally exhibits 12 convection cells of roughly unit aspect ratio but, unlike Model A1-fs, is highly time-dependent. Model Bfs shows a preference for drifting into a convective pattern arranged into 24 convection cells so that the time-averaged mean cell width in Model Bfs agrees closely with Model B1-fs.

The similarly sized convection cells in Models A1-fs and Afs and Models B1-fs and Bfs result in these pairs of models yielding very similar time-averaged mean temperatures.

In contrast, the pattern of convection observed in Model Cfs differs from Model C1-fs by the greatest wavelength that the box size in Model Cfs will permit. More specifically, the convective flow in Model Cfs is time-dependent but remains in a two-cell pattern characterized by a pair of equally sized convection cells with aspect ratios of six. Despite the long-wavelength convection characterizing this model, the mean temperature is actually lower in the aspect ratio 12 model than in the aspect ratio 1 model.

Temperature field snapshots of free-slip boundary convection in unit aspect ratio boxes with reflecting sidewalls. A steady-state solution is obtained. Isoviscous convection with an isothermal bottom boundary and uniformly distributed internal heat sources.

A time-dependent solution is obtained. Convection with a depth-dependent viscosity that increases monotonically from top to bottom by a factor of The bottom boundary of the calculation is isothermal, internal heat sources are distributed uniformly. Temperature field snapshots of free-slip boundary convection in aspect ratio 12 boxes with periodic wrap-around boundary conditions. All three solutions are time-dependent.

The bottom boundary of the calculation is isothermal and internal heat sources are distributed uniformly. The cooling influence of a viscosity that increases with depth has been described in previous mantle convection studies e. Velocities in the lower thermal boundary layer are retarded by the high viscosity at the base of the box, and the role of advection in the transfer of heat is reduced.

In comparison, downwellings are able to form more easily in the less viscous upper thermal boundary layer. The difference in the heat flow at the two boundaries can be viewed in terms of the local Rayleigh numbers of the thermal boundary layers.

The Rayleigh number characterizing the boundary layer is obtained by replacing the layer depth in eq. Since the viscosity at the bottom of the boxes in Models C1-fs and Cfs is 36 times greater than that at the top, the lower boundary layer can thicken to 3. Consequently, the effect of the depth-dependent viscosity is to allow the boundary layer at the base of the box to translate further laterally before becoming unstable than the boundary layer at the top of the box velocities at the two boundaries will differ so an exact estimate of how much further cannot be obtained.

The net result is that short-wavelength instabilities form at the top boundary and cool the depth-dependent viscosity models efficiently and long-wavelength instabilities appear at the bottom boundary and do not heat the models as efficiently as they are cooled.

By decreasing the aspect ratio of a Case C convection model, drips from the upper thermal boundary layer that cool the model interior become less influential since fewer drips can form in a small box. Thus Model C1-fs is warmer than Model Cfs. Model A1 is a per cent basally heated isoviscous model with one plate.

The mean temperature and heat flow calculated from Model A1 in Table 1 agree with the mean temperature and heat flow from Model A1-fs to within 2 per cent. We suggest that the similarity between the free-slip model and a model incorporating a plate with a width equal to the free-slip convection model cell size verifies that our plate formulation neither drives nor retards the mantle circulation. Models A1 and A1-fs are the only examples in this study of a pair of models, with and without a plate, of the same case and aspect ratio where the mantle circulation is continually moving in the same direction and the same characteristic convective wavelength is maintained.

Like Model A1, the two smallest aspect ratio Case A models with plates aspect ratios 0. The presence of the plates in the three widest models aspect ratios 2, 3 and 5 suppresses instabilities in the upper thermal boundary layers and allows single-cell flow to prevail. In contrast, Case A models with free-slip surfaces develop into multicell flows when aspect ratios of 2, 3 and 5 are specified.

Table 1 shows that as the aspect ratio of these models increases, the mean temperature of the models increases and the average surface heat flux decreases. These authors attributed the temperature increase in wider boxes to the dissimilar nature of the heat transport across the upper and lower boundaries of the models. Their argument is fundamentally the same as the argument given in the previous section to explain why a convecting system with a viscosity that increases with depth is cooler on average than an isoviscous convecting fluid.

The suppression of vertical velocity in the viscous plates increases the stability of the upper thermal boundary layer and results in a continued thickening of the boundary layer and reduced heat flow over the width of the model. In contrast, heat flow across the less viscous boundary layer at the bottom of the box is more efficient.

Thus, to balance the heat transfer, the mean temperature of the box increases. Table 1 indicates the variability that occurs in heat flow and temperature in different aspect ratio models. A large part of this variability is the result of episodic flow reversals that occur in the internally heated models. We define a flow reversal as a change in the direction of the mantle circulation e. Models characterized by flow reversals are identified in Table 1 by a superscript R.

The nature of the flow reversals ranges from perfectly periodic to totally unpredictable. In general, we find that increasing the aspect ratios of our models reduces the frequency of the reversals. For example, flow reversals occur in all of the aspect ratio 0. We find the same result when a step function increase in viscosity is specified at a depth of km assuming a mantle depth of km in place of the gradual viscosity increase used in the Case C models.

When viscosity is increased by a factor of 30 at km, flow reversals are observed in aspect ratio 1 models but not aspect ratio 3 models. Thus we find that, independent of the gradient of the viscosity increase, a stiff lower mantle acts to stabilize convection patterns in larger aspect ratio models but has little discernible effect on the frequency of flow reversal events in unit aspect ratio models. This model, B1 in Table 1 , differs from Model B1-fs only by the presence of a plate.

The relatively sudden draining of the upper thermal boundary layer entrains a hot parcel of fluid trapped below the viscous plate and drags it into the lower mantle.

As the hot material rises it begins to push the plate to the right and material in the cold thermal boundary layer flushes into the mantle at the right-hand side of the box c. In d , buoyant material has been entrained with the new downwelling; however, the entrained buoyant material again rises and reverses the flow direction once the intensity of the initial flushing event diminishes e.

In f the cycle is about to repeat. The time required to complete the cycle is approximately Myr. This type of behaviour is unique to internally heated models with plates and appears to be driven by the plates trapping internally generated heat in the cores of convection cells that are wider than those found in free-slip boundary condition models.

Model B1. Temperature fields from a period covering a single cycle from a model in which flow reverses twice. The model has an aspect ratio of 1. The plate has a specified viscosity that is times more viscous than the isoviscous mantle below.

Times corresponding to the panels in Fig. Heat moves from areas of higher temperature to areas of lower temperature. The three mechanisms for heat transfer are radiation, conduction and convection. Radiation moves energy without contact between particles, like the radiation of energy from the Sun to the Earth through the vacuum of space. Conduction transfers energy from one molecule to another through contact, without particle movement, as when sun-warmed land or water heats the air directly above.

Convection occurs through the movement of particles. As particles become heated, the molecules move faster and faster, and as molecules move apart, density decreases. The warmer, less dense material rises compared to the surrounding cooler, higher density material. While convection generally refers to the fluid flow occurring in gases and liquids, convection in solids like the mantle occurs but at a slower rate.

Heat in the mantle comes from the Earth's molten outer core, decay of radioactive elements and, in the upper mantle, friction from descending tectonic plates. The heat in the outer core results from residual energy from the Earth's formative events and the energy generated by decaying radioactive elements.

At the mantle-crust boundary. The temperature difference between the upper and lower boundaries of the mantle requires heat transfer to occur. The trench may be several to six miles up to 10 or more kilometers deep below the average level of the seafloor in the region and marks the boundary between the overriding and underthrusting plate.

The outer trench slope is the region from the trench to the top of the flexed oceanic crust that forms a several hundred to one-thousand-foot few hundred-meter high topographic rise known as the forebulge on the downgoing plate.

Trench floors are triangular shaped in profile and typically are partly to completely filled with grey-wacke-shale turbidite sediments derived from erosion of the accretionary wedge. They may also be transported by currents along the trench axis for large distances, up to hundreds or even thousands of miles thousands of kilometers from their ultimate source in uplifted mountains in the convergent orogen.

Flysch is a term that applies to rapidly deposited deep marine syn-orogenic clastic rocks that are generally turbidites. Trenches are also characterized by chaotic deposits known as olistostromes that typically have clasts or blocks of one rock type, such as limestone or sandstone, mixed with a muddy or shaly matrix. These are interpreted as slump or giant submarine landslide deposits. They are common in trenches because of the oversteepening of slopes in the wedge.

The sediments are deposited as flat-lying turbi-dite packages, then gradually incorporated into the accretionary wedge complex through folding and the propagation of faults through the trench sediments.

It causes the rotation and uplift of the accretionary prism, which is a broadly steady-state process that continues as long as sediment-laden trench deposits are thrust deeper into the trench. Typically new faults will form and propagate beneath older ones, rotating the old faults and structures to steeper attitudes as new material is added to the toe and base of the accretionary wedge. This process increases the size of the overriding accre-tionary wedge and causes a seaward-younging in the age of deformation.

Parts of the oceanic basement to the subducting slab are sometimes scraped off and incorporated into the accretionary prisms. These tectonic slivers typically consist of fault-bounded slices of basalt, gabbro, and ultramafic rocks, and rarely, partial or even complete ophiolite sequences can be recognized. Major differences in processes occur at Andean-style compared to Marianas-style arc systems.

Andean-type arcs have shallow trenches, fewer than 3. Andean arcs have back-arc regions dominated by foreland retroarc fold thrust belts and sedimentary basins, whereas marianas-type arcs typically have.

Andean arcs have thick crust, up to Andean arcs have only rare volcanoes, and these have magmas rich in sio2 such as rhyolites and andesites. Plutonic rocks are more common, and the basement is continental crust. Marianas-type arcs have many volcanoes that erupt lava low in silica content, typically basalt, and are built on oceanic crust. Many arcs are transitional between the Andean or continental-margin types and the oceanic or Marianas types, and some arcs have large amounts of strike-slip motion.

The causes of these variations have been investigated and it has been determined that the rate of convergence has little effect, but the relative motion directions and the age of the subducted oceanic crust seem to have the biggest effects. In particular old oceanic crust tends to sink to the point where it has a near-vertical dip, rolling back through the viscous mantle and dragging the arc and forearc regions of overlying Marianas-type arcs with it.

This process contributes to the formation of back arc basins.